Related papers: On Using The Two-Way Cluster-Robust Standard Error…
Likelihood fitting to two-point clustering statistics made from galaxy surveys usually assumes a multivariate normal distribution for the measurements, with justification based on the central limit theorem given the large number of…
Many systems in nature are conjectured to exist at a critical point, including the brain and earthquake faults. The primary reason for this conjecture is that the distribution of clusters (avalanches of firing neurons in the brain or…
In recent machine learning systems, confidence scores are being utilized more and more to manage selective prediction, whereby a model can abstain from making a prediction when it is unconfident. Yet, conventional metrics like accuracy,…
Cluster standard error (Liang and Zeger, 1986) is widely used by empirical researchers to account for cluster dependence in linear model. It is well known that this standard error is biased. We show that the bias does not vanish under high…
In this manuscript we consider the problem of generalized linear estimation on Gaussian mixture data with labels given by a single-index model. Our first result is a sharp asymptotic expression for the test and training errors in the…
Clustering is a fundamental tool in statistical machine learning in the presence of heterogeneous data. Most recent results focus primarily on optimal mislabeling guarantees when data are distributed around centroids with sub-Gaussian…
This paper considers the problem of estimating the variance of a sum of a triangular array of random vectors with heterogeneous means. When random vectors exhibit two-way cluster dependence or weak dependence, standard variance estimators…
We consider the sampling of the coupled cluster expansion within stochastic coupled cluster theory. Observing the limitations of previous approaches due to the inherently non-linear behaviour of a coupled cluster wavefunction representation…
A central limit theorem for arrays of symmetric row-wise exchangeable random variables is presented. The result is valid for finite and infinite extendable and non-extendable sequences. Unlike most reported versions of the central limit…
Motivated by modern applications in which one constructs graphical models based on a very large number of features, this paper introduces a new class of cluster-based graphical models, in which variable clustering is applied as an initial…
Robustly determining the optimal number of clusters in a data set is an essential factor in a wide range of applications. Cluster enumeration becomes challenging when the true underlying structure in the observed data is corrupted by…
In this paper, we prove a central limit theorem and estabilish a moderate deviation principle for stochastic models of incompressible second fluids. The weak convergence method inreoduced by [4] plays an important role.
When using a finite difference method to solve an initial--boundary--value problem, the truncation error is often of lower order at a few grid points near boundaries than in the interior. Normal mode analysis is a powerful tool to analyze…
The aim of this Thesis is to present five new tests for random numbers, which are widely used {\em e.g.} in computer simulations in physics applications. The first two tests, the cluster test and the autocorrelation test, are based on…
Let $(X_{n,i})_{1\le i\le n,n\in\mathbb{N}}$ be a triangular array of row-wise stationary $\mathbb{R}^d$-valued random variables. We use a "blocks method" to define clusters of extreme values: the rows of $(X_{n,i})$ are divided into $m_n$…
We consider linear two-time-scale stochastic approximation algorithms driven by martingale noise. Recent applications in machine learning motivate the need to understand finite-time error rates, but conventional stochastic approximation…
A two-variable stochastic model for diffusion-limited nucleation is developed using a formalism derived from fluctuating hydrodynamics. The model is a direct generalization of the standard Classical Nucleation Theory. The nucleation rate…
We introduce an efficient scheme to correct errors due to the finite squeezing effects in continuous-variable cluster states. Specifically, we consider the typical situation where the class of algorithms consists of input states that are…
This paper is devoted to the Gaussian fluctuations and deviations of the traces of tridiagonal random matrix. Under quite general assumptions, we prove that the traces are approximately normal distributed. Multi-dimensional central limit…
This article proposes a novel variance estimator for within-cluster resampling (WCR) and modified within-cluster resampling (MWCR) - two existing methods for analyzing longitudinal data. WCR is a simple but computationally intensive method,…